arXiv subjects

Hunter Swan

Publications and source records attributed to Hunter Swan.

12 recordsLinked to original sources

arXiv2026

Symmetry Promotion in Electromagnetism

A symmetric distribution of charges or currents typically produces an electromagnetic field having the same symmetry group. However, under special circumstances we show that a discrete symmetry of the source distribution leads to a larger continuous symmetry for the resulting field in restricted regions. The conditions for this promotion from discrete to continuous symmetry are that the fields be affine linear and the symmetry of the source distribution act irreducibly on the ambient space. We illustrate this effect with many examples. This phenomenon is pedagogically interesting both as a source of inspiration in electro- and magnetostatics and as an accessible example of group representation theory.

physics.class-ph↗

arXiv2026

Exact Semiclassical Phase Shifts for Relativistic Atom Interferometers in Flat Spacetime

Atom interferometry is a sensitive tool for measuring relativistic effects, but there are no known non-trivial exact solutions for relativistic atom interferometer phase shifts. Here we derive relativistically exact expressions within the usual semiclassical approximation for a wide range of experimentally interesting atom interferometer pulse sequences in flat spacetime, including Mach-Zehnder, resonant, and large momentum transfer interferometer geometries. As an example, the leading order phase shift $\omega_a g T^2/c$ for a Mach-Zehnder clock atom interferometer is found to become $\omega_a \left(1 + \frac{\omega_a}{2m}\right)(e^{-gT/c}-1)^2 c/g$ when all relativistic kinematics are included. We calculate exact phase shifts for both clock (single-photon) interferometers and Raman or Bragg (two-photon) interferometers.

physics.atom-ph↗

arXiv2025

A fast, large-scale optimal transport algorithm for holographic beam shaping

Optimal transport methods have recently established state of the art accuracy and efficiency for holographic laser beam shaping. However, use of such methods is hindered by severe $\mathcal{O}(N^2)$ memory and $\mathcal{O}(N^2)$ time requirements for large scale input or output images with $N$ total pixels. Here we leverage the dual formulation of the optimal transport problem and the separable structure of the cost to implement algorithms with greatly reduced $\mathcal{O}(N)$ memory and $\mathcal{O}(N\log N)$ to $\mathcal{O}(N^{3/2})$ time complexity. These algorithms are parallelizable and can solve megapixel-scale beam shaping problems in tens of seconds on a CPU or seconds on a GPU.

physics.optics↗

arXiv2025

Atom Interferometer Phase Shear and Spacetime Sectional Curvature

Atom interferometry is a natural laboratory for precision tests of general relativity, but there is no simple relationship between atom interferometer phase and geometric properties of spacetime. Here we show that a different atom interferometer observable, the phase shear, can be expressed directly as the integrated sectional curvature over a spacetime surface enclosed by the interferometer arms and final beamsplitter. This is a consequence of a generalized Gauss-Bonnet theorem, which also explicitly computes small correction terms arising from gravitational redshift of atom optics pulses. This synthesis of quantum mechanics, relativity, and differential geometry affords a manifestly coordinate-free and representation-free means of measuring spacetime properties. Additionally, it provides a convenient computational tool for predicting atom interferometer properties in arbitrary background spacetimes.

physics.atom-ph↗

arXiv2024

High-fidelity holographic beam shaping with optimal transport and phase diversity

A phase-only spatial light modulator (SLM) provides a powerful way to shape laser beams into arbitrary intensity patterns, but at the cost of a hard computational problem of determining an appropriate SLM phase. Here we show that optimal transport methods can generate approximate solutions to this problem that serve as excellent initializations for iterative phase retrieval algorithms, yielding vortex-free solutions with superior accuracy and efficiency. Additionally, we show that analogous algorithms can be used to measure the intensity and phase of the input beam incident upon the SLM via phase diversity imaging. These techniques furnish flexible and convenient solutions to the computational challenges of beam shaping with an SLM.

physics.optics↗

arXiv2024

Collinear Three-Photon Excitation of a Strongly Forbidden Optical Clock Transition

The ${{^1\mathrm{S}_0}\!-\!{^3\mathrm{P}_0}}$ clock transition in strontium serves as the foundation for the world's best atomic clocks and for gravitational wave detector concepts in clock atom interferometry. This transition is weakly allowed in the fermionic isotope $^{87}$Sr but strongly forbidden in bosonic isotopes. Here, we demonstrate coherent excitation of the clock transition in bosonic ${}^{88}$Sr using a novel collinear three-photon process in a weak magnetic field. We observe Rabi oscillations with frequencies of up to $50~\text{kHz}$ using $\text{W}/\text{cm}^{2}$ laser intensities and Gauss-level magnetic field amplitudes. The absence of nuclear spin in bosonic isotopes offers decreased sensitivity to magnetic fields and optical lattice light shifts, enabling atomic clocks with reduced systematic errors. The collinear propagation of the laser fields permits the interrogation of spatially separated atomic ensembles with common laser pulses, a key requirement for dark matter searches and gravitational wave detection with next-generation quantum sensors.

physics.atom-ph↗

arXiv2023

Atom Interferometry with Floquet Atom Optics

Floquet engineering offers a compelling approach for designing the time evolution of periodically driven systems. We implement a periodic atom-light coupling to realize Floquet atom optics on the strontium ${}^1\!S_0\,\text{-}\, {}^3\!P_1$ transition. These atom optics reach pulse efficiencies above $99.4\%$ over a wide range of frequency offsets between light and atomic resonance, even under strong driving where this detuning is on the order of the Rabi frequency. Moreover, we use Floquet atom optics to compensate for differential Doppler shifts in large momentum transfer atom interferometers and achieve state-of-the-art momentum separation in excess of $400~\hbar k$. This technique can be applied to any two-level system at arbitrary coupling strength, with broad application in coherent quantum control.

physics.atom-ph↗

arXiv2021

Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100)

MAGIS-100 is a next-generation quantum sensor under construction at Fermilab that aims to explore fundamental physics with atom interferometry over a 100-meter baseline. This novel detector will search for ultralight dark matter, test quantum mechanics in new regimes, and serve as a technology pathfinder for future gravitational wave detectors in a previously unexplored frequency band. It combines techniques demonstrated in state-of-the-art 10-meter-scale atom interferometers with the latest technological advances of the world's best atomic clocks. MAGIS-100 will provide a development platform for a future kilometer-scale detector that would be sufficiently sensitive to detect gravitational waves from known sources. Here we present the science case for the MAGIS concept, review the operating principles of the detector, describe the instrument design, and study the detector systematics.

physics.atom-ph↗

arXiv2020

Large Momentum Transfer Clock Atom Interferometry on the 689 nm Intercombination Line of Strontium

We report the first realization of large momentum transfer (LMT) clock atom interferometry. Using single-photon interactions on the strontium ${}^1S_0 - {}^3P_1$ transition, we demonstrate Mach-Zehnder interferometers with state-of-the-art momentum separation of up to $141\,\hbar k$ and gradiometers of up to $81\,\hbar k$. Moreover, we circumvent excited state decay limitations and extend the gradiometer duration to 50 times the excited state lifetime. Because of the broad velocity acceptance of the interferometry pulses, all experiments are performed with laser-cooled atoms at a temperature of $3\,μ\text{K}$. This work has applications in high-precision inertial sensing and paves the way for LMT-enhanced clock atom interferometry on even narrower transitions, a key ingredient in proposals for gravitational wave detection and dark matter searches.

physics.atom-ph↗

arXiv2018

Nonnegative Eigenvectors of Symmetric Matrices

For matrices with all nonnegative entries, the Perron-Frobenius theorem guarantees the existence of an eigenvector with all nonnegative components. We show that the existence of such an eigenvector is also guaranteed for a very different class of matrices, namely real symmetric matrices with exactly two eigenvalues. We also prove a partial converse, that among real symmetric matrices with any more than two eigenvalues there exist some having no nonnegative eigenvector.

math.RA↗

arXiv2018

Expected Number of Vertices of a Hypercube Slice

Given a random k-dimensional cross-section of a hypercube, what is its expected number of vertices? We show that, for a suitable distribution of random slices, the answer is $2^k$, independent of the dimension of the hypercube.

math.PR↗

arXiv2015

"Irregularization" of Systems of Conservation Laws

We explore new ways of regulating defect behavior in systems of conservation laws. Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt to control defects by making them smoother, our schemes result in defects which are \textit{more singular}, and we thus refer to such schemes as "irregularizations". In particular, we seek to produce \textit{delta shock} defects which satisfy a condition of \textit{stationarity}. We are motivated to pursue such exotic defects by a physical example arising from dislocation dynamics in materials physics, which we describe.

math.AP↗